Finding an oscillator's period with a dataset in Mathematica

1. The problem statement, all variables and given/known data
I have a dataset of an oscillator with 51 measurements, I uploaded it here. It's in the form of {time, position}. I have to find the period of this oscillator in Mathematica.

2. Relevant equations
I have to use the NonLinearRegress function to find it.

3. The attempt at a solution
I started with the following code:

Code (Text):

data = {oscdata};
{tdata, xdata} = Transpose[data]

1. The problem statement, all variables and given/known data
That gives me the first problem, because I get an error saying the two lists are not the same shape, while they clearly are. Anyone know why that's happening?

Code (Text):

"Lists {tdata,xdata} and \
{{{0,0.369}},{{0.1,0.0999}},{{0.2,0.0904}},{{0.3,-0.054}},{{0.4,-0.1}}\
,{{0.5,-<<6>>}},{{0.6,-0.328}},{{0.7,-0.388}},{{0.8,-0.486}},{{0.9,-0.\
576}},<<51>>} are not the same shape"